I doubt we'll see many, if any, RARE games on any hypothetical N64 Mini. MS have released RARE Replay with Banjo, etc. on it, although there may be a chance for the 'shared IP' games e.g. DK64.
The downside to real hardware is that it can quickly become a pain e.g. choosing a 'better' model, HDMI conversion (if necessary), stereo sound, wear and tear, etc. and on top of this you'll need a flash cart if you want ROMs on it.
Personally, I'd just look at finding a decent emulator unless you really want the most 'authentic' experience and willing to put the money/effort in.